Nonstationary pattern-based signal-noise separation using adaptive prediction-error filter

Introduction

During seismic data acquisition, complex field conditions unavoidably lead to several interferences. For instance, wind motion and electronic noise from geophones cause random noise, propagation of seismic waves on land near the surface leads to ground-roll noise. Meanwhile, it is natural that geologic events and geophysical data exhibit nonstationarity, which is manifested in several intrinsic properties, e.g. spectra and statistical characteristics, and change with time and space. To reduce the influences of noise and improve the quality of useful signal for subsequent data processing and interpretation, the signal-noise separation is always an important procedure, especially in new acquisition techniques such as distributed acoustic sensing.

Many effective methods have been proposed for eliminating seismic random noise besides mean and median filters tailored to images. According to the different properties of target signals, several transform methods can truncate the energy in the transform domain to suppress random noise, such as radon transform (Claerbout and Johnson, 1971; Trad et al., 2002), curvelet transform (Kumar and Herrmann, 2009) and seislet transform (Fomel and Liu, 2010; Liu et al., 2015). Prediction filters are effective methods for random noise attenuation, which was first introduced by Canales (1984). The prediction process can be achieved in the time-space domain or the frequency-space domain (Wang, 1999). Liu and Li (2018) proposed a fast-streaming prediction filter to attenuate random noise. Recently, the deep-learning method has also been found to cope with the denoising procedure; Yu et al. (2019) developed a deep-learning method for random noise attenuation by using a convolutional neural network.

Ground-roll noise is a strong coherent noise, which will interfere with land seismic surveys. Frequency-based filtering and F-K filtering are the classical methods to handle ground- roll noise problem. Wavelet transform (Corso et al., 2003; Miao and Cheadle, 1998) and curvelet transform (Naghizadeh and Sacchi, 2018) are practical methods for ground-roll removal as well. Time-frequency analysis can separate different components by using a muting filter in the time-frequency domain, Liu and Fomel (2013) applied this method to separate the ground-roll noise from the field data. Using a generator and discriminator, a generative adversarial network (GAN) can be trained to produce a noise-free result, Yuan et al. (2020) developed GAN for ground-roll noise removal.

A pattern-based method is often used for signal-noise separation. Spitz (1999) described a multiple subtraction technology by using a pattern recognition method. Bednar and Neale (1999) made a comparison of a pattern-based multiple suppression method and other approaches. Brown and Clapp (2000) used a pattern-based method with nonstationary prediction-error filter (PEF) for ground-roll removal. Guitton (2006) further implemented such a pattern-based approach to separate multiples in a 3D dataset.

In this paper, we revisit the fundamental theory behind the pattern-based signal-noise separation method (Claerbout, 2010) and extend this with an adaptive prediction-error filter (APEF). The pattern-based method (Brown and Clapp, 2000; Claerbout and Fomel, 2000) estimates operators to characterize data patterns, and then solves the signal-noise separation problem. Similarly, we exploited the pattern-based method but calculated the APEF (Liu et al., 2011) to represent the pattern of nonstationary data and the noise model. Different algorithms were adopted to deal with random noise and ground-roll noise, and we tested the nonstationary characteristics of the proposed method in synthetic models and field data examples. Results of random noise attenuation and ground-roll removal on these examples demonstrated that the pattern-based signal-noise separation with the nonstationary APEF is effective in separating noise from signal.

Nonstationary pattern-based signal-noise separation using adaptive prediction-error filter